Building Models for Stratigraphic Paleobiology in R

Stratigraphic Paleobiology

The fossil record is a joint expression of

  • Stratigraphy
  • Preservation
  • Biology (ecology & evolution)

Example: evolution in the time domain

Example: evolution in the stratigraphic domain

Aims

Combine models of stratigraphy with evolutionary biology and ecology into stratigraphic paleobiology modeling pipelines

Focus:

  1. Age-depth models and incompleteness

  2. Trait evolution

  3. Fossil abundance, ecology, and last occurrences

Example data

Age-depth models (ADMs)

Piping

rnorm(500) |>                          # generate 500 normally distributed random numbers
  hist(main = "Normal distribution")   # plot histogram

|> is the pipe operator
Read the code like text!

Piping example

seq(from = 0, to = 1, by = 0.01) |>  # fix time steps of evaluation
  random_walk() |>                   # simulate random walk
  plot(type = "l",                   # plot results
       xlab = "Time",
       ylab = "Value",
       lwd = 2)

Tasks ADMs and incompleteness (45 min)

  1. Define age-depth models for different locations along the onshore-offshore gradient, and plot them.
    • How do they connect to the chronostratigraphic diagram and the sea level curve?
  2. Examine how stratigraphic incompleteness and the number of hiatuses changes along the onshore-offshore gradient.
  3. Generate histograms of hiatus durations at the different distances from shore.
    • Do you see any systematic changes?

Results

Break (15 min)

Trait evolution

Traits are measurable characteristics of an organism
How do traits evolve in a lineage?

Modes of evolution

  • Stasis - no net change

  • Random walk - random accumulation of change

  • Ornstein-Uhlenbeck (OU) process - convergence towards an optimum

Question

  • How do stratigraphic biases change our perception of the mode of evolution?

Tasks trait evolution (45 min)

  1. Plot the different modes of evolution in the time domain.

    • What is their internal variation due to randomness (i.e., how much do results differ if you plot them multiple times)?
    • What is the biological meaning of the model parameters?

  2. Transform the different modes of evolution into the stratigraphic domain and plot them.

    • Which modes are most/least affected by stratigraphic biases?
    • Do you see any systematic changes?

Results

Break (15 min)

Niche modeling and last occurrences

  • Taxa track their preferred niche

  • Environmental conditions at a place change with time

Questions

  • How does ecology change fossil abundance?

  • How does stratigraphy influence extinction rate estimates?

Tasks ecology and last occurrences (45 min)

Ecology

  1. Simulate an abundant taxon, and transform the fossil ages into the stratigraphic domain.
    • At which locations and stratigraphic heights do you observe peaks in fossil abundance?
    • With which stratigraphic effects are these peaks associated?
  2. Define a niche for a taxon, and add the niche model to your pipeline.
    • How and why do your results change?
    • How could you misinterpret the results?

Tasks ecology and last occurrences (45 min)

Last occurrences

  1. Simulate last occurrences based on the assumption of a constant rate of last occurrences and transform them into the stratigraphic domain.
    • Where do you observe clusters of last occurrences?
    • With what stratigraphic effects are these locations associated?
    • How would you misinterpret the results in the absence of stratigraphic information? Use your results to formulate a “stratigraphic null hypothesis” for clusters of last occurrences.

Results

Advanced usage

  • Other forward models
  • Other biological models (niches, trait evolution)
  • Other data structures (phylogenetic trees)

Contributors welcome!

References

Burgess, Peter. 2013. “CarboCAT: A Cellular Automata Model of Heterogeneous Carbonate Strata.” Computers & Geosciences 53: 129–40. https://doi.org/https://doi.org/10.1016/j.cageo.2011.08.026.
———. 2023. “CarboCATLite.” Zenodo. https://doi.org/10.5281/zenodo.8402578.
Hohmann, Niklas, Joël R. Koelewijn, Peter Burgess, and Emilia Jarochowska. 2024. “Identification of the Mode of Evolution in Incomplete Carbonate Successions.” BMC Ecology and Evolution 24 (1): 113. https://doi.org/10.1186/s12862-024-02287-2.
Patzkowsky, Mark E, and Steven M Holland. 2012. Stratigraphic Paleobiology: Understanding the Distribution of Fossil Taxa in Time and Space. University of Chicago Press.